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Abstract

Issues of Ge hut cluster array formation and growth at low temperatures on the Ge/Si(001)
wetting layer are discussed on the basis of explorations performed by high resolution
STM and in-situ RHEED. Dynamics of the RHEED patterns in the process of Ge hut array formation is
investigated at low and high temperatures of Ge deposition. Different dynamics of
RHEED patterns during the deposition of Ge atoms in different growth modes is observed,
which reflects the difference in adatom mobility and their ‘condensation’ fluxes from
Ge 2D gas on the surface for different modes, which in turn control the nucleation
rates and densities of Ge clusters. Data of HRTEM studies of multilayer Ge/Si heterostructures
are presented with the focus on low-temperature formation of perfect films.

Heteroepitaxial Si p–i–n-diodes with multilayer stacks of Ge/Si(001) quantum dot dense arrays built in intrinsic
domains have been investigated and found to exhibit the photo-emf in a wide spectral
range from 0.8 to 5 μm. An effect of wide-band irradiation by infrared light on the photo-emf spectra has
been observed. Photo-emf in different spectral ranges has been found to be differently
affected by the wide-band irradiation. A significant increase in photo-emf is observed
in the fundamental absorption range under the wide-band irradiation. The observed
phenomena are explained in terms of positive and neutral charge states of the quantum
dot layers and the Coulomb potential of the quantum dot ensemble. A new design of
quantum dot infrared photodetectors is proposed.

By using a coherent source spectrometer, first measurements of terahertz dynamical
conductivity (absorptivity) spectra of Ge/Si(001) heterostructures were performed
at frequencies ranged from 0.3 to 1.2 THz in the temperature interval from 300 to
5 K. The effective dynamical conductivity of the heterostructures with Ge quantum
dots has been discovered to be significantly higher than that of the structure with
the same amount of bulk germanium (not organized in an array of quantum dots). The
excess conductivity is not observed in the structures with the Ge coverage less than
8 Å. When a Ge/Si(001) sample is cooled down the conductivity of the heterostructure
decreases.

Introduction

Artificial low-dimensional nano-sized objects, like quantum dots, quantum wires and
quantum wells, as well as structures based on them, are promising systems for improvement
of existing devices and for development of principally new devices for opto-, micro-
and nano-electronics. Besides, the investigation of physical properties of such structures
is also of fundamental importance. In both regards, amazing perspectives are provided
when playing around with quantum dots that can be considered as artificial atoms with
a controlled number of charge carriers that have a discrete energy spectrum
[1,2]. Arrays of a large number of quantum dots including multilayer heterostructures make it possible to
create artificial “solids” whose properties can be controllably changed by varying
the characteristics of constituent elements (“atoms”) and/or the environment (semiconductor
matrix). The rich set of exciting physical properties in this kind of systems originates
from single-particle and collective interactions that depend on the number and mobility
of carriers in quantum dots, Coulomb interaction between the carriers inside a quantum
dot and in neighbouring quantum dots, charge coupling between neighbouring quantum
dots, polaron and exciton effects, etc. Since characteristic energy scales of these
interactions (distance between energy levels, Coulomb interaction between charges
in quantum dots, one- and multiparticle exciton and polaron effects, plasmon excitations,
etc.) are of order of several meV
[3-5], an appropriate experimental tool for their study is provided by optical spectroscopy
in the far-infrared and terahertz bands.

To get access to the effects, one has to extend the operation range of the spectrometers
to the corresponding frequency domain that is to the terahertz frequency band. Because
of inaccessibility of this band, and especially of its lowest frequency part, below
1 THz (that is
cm−1), for standard infrared Fourier-transform spectrometers, correspondent data is presently
missing in the literature. In this paper, we present the results of the first detailed
measurements of the absolute dynamical (AC) conductivity of multilayer Ge/Si heterostructures
with Ge quantum dots, at terahertz and sub-terahertz frequencies and in the temperature
range from 5 to 300 K.

In addition, for at least two tens of years, multilayer Ge/Si heterostructures with
quantum dots have been candidates to the role of photosensitive elements of monolithic
IR arrays promising to replace and excel platinum silicide in this important brunch
of the sensor technology
[6-8]. Unfortunately, to date achievements in this field have been less than modest.

We believe that this state of affairs may be improved by rigorous investigation of
formation, defects and other aspects of materials science of such structures, especially
those which may affect device performance and reliability, focusing on identification
of reasons of low quantum efficiency and detectivity, high dark current and tend to
degrade with time as well as on search of ways to overcome these deficiences. New
approaches to device architecture and design as well as to principles of functioning
are also desirable.

This article reports our latest data on morphology and defects of Ge/Si heterostructures.
On the basis of our recent results on the photo-emf in the Si p–i–n-structures with Ge quantum dots, which are also reported in this article, we propose
a new design of photovoltaic quantum dot infrared photodetectors.

Methods

Equipment and techniques

The Ge/Si samples were grown and characterized using an integrated ultrahigh vacuum
instrument
[9-12] built on the basis of the Riber SSC 2 surface science center with the EVA 32 molecular-beam
epitaxy (MBE) chamber equipped with the RH20 reflection high-energy electron diffraction
(RHEED) tool (Staib Instruments) and connected through a transfer line to the GPI-300
ultrahigh vacuum scanning tunnelling microscope (STM)
[13-15]. Sources with the electron beam evaporation were used for Ge or Si deposition. A
Knudsen effusion cells was utilized if boron doping was applied for QDIP p–i–n-structure formation. The pressure of about 5×10−9 Torr was kept in the preliminary sample cleaning (annealing) chamber. The MBE chamber
was evacuated down to about 10−11 Torr before processes; the pressure increased to nearly 2×10−9 Torr at most during the Si substrate cleaning and 10−9 Torr during Ge or Si deposition. The residual gas pressure did not exceed 10−10 Torr in the STM chamber. Additional details of the experimental instruments and process
control can be found in Ref.
[12].

RHEED measurements were carried out in situ, i.e., directly in the MBE chamber during a process
[10]. STM images were obtained in the constant tunnelling current mode at the room temperature.
The STM tip was zero-biased while the sample was positively or negatively biased when
scanned in empty- or filled-states imaging mode. Structural properties of the Ge/Si
films were explored by using the Carl Zeiss Libra-200 FE HR HRTEM.

For obtaining spectra of photo-electromotive force (photo-emf) a setup enabling sample
illumination by two independent beams was used; one of the beams was a wide-band infrared
(IR) radiation, generated by a tungsten bulb, passed through a filter of Si or Ge
(bias lighting) and the other was a beam-chopper modulated narrow-band radiation cut
from globar emission by an IR monochromator tunable in the range from 0.8 to 20 μm. The spectra were taken at the chopping frequency of 12.5 Hz at temperatures ranged
from 300 to 70 K and a widely varied power of the bias lighting.

The measurements of the terahertz dynamic conductivity and absorptivity of Ge/Si heterostructures
at room and cryogenic temperatures (down to 5 K) have been performed using the spectrometer
based on backward-wave oscillators (BWO) as radiation sources. This advanced experimental
technique will be described in detail below in a separate section.

Sample preparation procedures

Preparation of samples for STM and RHEED

Initial samples for STM and RHEED studies were 8×8 mm2 squares cut from the specially treated commercial boron-doped Czochralski-grown (CZ)
Si(100) wafers (p-type, ρ=12 Ω cm). After washing and chemical treatment following the standard procedure described
elsewhere
[17], which included washing in ethanol, etching in the mixture of HNO3 and HF and rinsing in the deionized water
[12], the silicon substrates were loaded into the airlock and transferred into the preliminary
annealing chamber where they were outgassed at the temperature of around 565℃ for
more than 6 h. After that, the substrates were moved for final treatment and Ge deposition
into the MBE chamber where they were subjected to two-stages annealing during heating
with stoppages at 600℃ for 5 min and at 800℃ for 3 min
[9,10]. The final annealing at the temperature greater than 900℃ was carried out for nearly
2.5 min with the maximum temperature of about 925℃ (1.5 min). Then, the temperature
was rapidly lowered to about 750℃. The rate of the further cooling was around 0.4℃/s
that corresponded to the ‘quenching’ mode applied in
[10]. The surfaces of the silicon substrates were completely purified of the oxide film
as a result of this treatment
[10,18,19].

Ge was deposited directly on the deoxidized Si(001) surface. The deposition rate was
varied from about 0.1 to 0.15 Å/s; the effective Ge film thickness (hGe) was varied from 3 to 18 Å for different samples. The substrate temperature during
Ge deposition (Tgr) was 360℃ for the low-temperature mode and 600 or 650℃ for the high-temperature mode.
The rate of the sample cooling down to the room temperature was approximately 0.4℃/s
after the deposition.

Preparation of multilayer structures

Ge/Si heterostructures with buried Ge layers were grown on CZ p-Si(100):B wafers (ρ =12 Ω cm) washed and outgassed as described above. Deoxidized Si(001) surfaces were
prepared by a process allowed us to obtain clean substrate surfaces (this was verified
by STM and RHEED) and perfect epitaxial interfaces with Si buffer layers (verified
by HRTEM): the wafers were annealed at 800℃ under Si flux of
Å/s until a total amount of the deposited Si, expressed in the units of the Si film
thickness indicated by the film thickness monitor, reached 30 Å; 2-minute stoppages
of Si deposition were made first twice after every 5 Å and then twice after every
10 Å.

Afterwards, a ∼ 100 nm thick Si buffer was deposited on the prepared surface at the
temperature of ∼ 650℃. Then, a single Ge layer or a multilayer Ge/Si structure was
grown. A number of Ge layers in multilayer structures reached 15 but usually was 5;
their effective thickness (hGe), permanent for each sample, was varied from sample to sample in the range from 4
to 18 Å; the thickness of the Si spacers (hSi) was ∼ 50 nm. The Ge deposition temperature was ∼ 360℃, Si spacers were grown at
∼ 530℃. A heterostructure formed in such a way was capped by a ∼ 100 nm thick Si layer
grown at ∼ 530℃. All layers were undoped.

The samples were quenched after the growth at the rate of ∼ 0.4℃/s.

Growth of p–i–n-structures

p–i–n-structures were grown on commercial phosphorus-doped CZ n-Si(100) substrates (ρ=0.1 Ω cm). Si surfaces were prepared for structure deposition in the same way as
for the growth of multilayer structures. i-Si buffer domains of various thicknesses were grown on the clean surfaces at ∼ 650℃.
Then, a stacked structure of several periods of quantum dot (QD) dense arrays separated
by Si barriers was grown under the same conditions as the multilayer structures; hSi was widely varied in different structures reaching 50 nm; hGe always was 10 Å. A sufficiently thick undoped Si layer separated the stacked QD array
from the Si:B cap doped during the growth, the both layers were grown at ∼ 530℃.

Figure
1 demonstrates two such structures (referred to as R 163 and R 166) which are in the
focus of this article. Their caps were doped to 5×1018 and 1019 cm−3 in the R 163 and R 166 samples, respectively. Buffer layer and barrier thicknesses
were 99 and 8 nm in the R 163 structure and 1690 and 30 nm in R 166.

Figure 1.Schematics of the p–i–n-structures. Stacks of five layers of Ge hut clusters (quantum dots) separated by Si barriers
are built in the intrinsic domains of the p–i–n diodes; the p–i–n mesa structures were formed on CZ n-Si(100) substrates (ρ=0.1 Ω cm); composition and thickness of each layer of the mesa structures as well
as locations of Al contacts are shown in the scatches; (a) in the R 163 structure, the boron concentration in the Si cap layer is ∼5×1018 cm−3; (b) the boron concentration in the Si cap layer of the R 166 structure is ∼1019 cm−3.

Mesas were formed on samples for photoelectric measurements. Ohmic contacts were formed
by thermal deposition of aluminum.

Terahertz BWO-spectroscopy

The BWO-spectrometers provide broad-band operation (frequencies ν ranging from 30 GHz to 2 THz), high frequency resolution (Δν/ν=10−5), broad dynamic range (40–50 dB), continuous frequency tuning and, very importantly,
the possibility of direct determination of spectra of any “optical” parameter, like complex conductivity, complex
dielectric permittivity, etc. (‘direct’ means that no Kramers–Kronig analysis—typical
for far-infrared Fourier transform spectroscopy—is needed). The principle of operation
of BWO-spectrometers is described in details in the literature (see, e.g.,
[20,21]). It is based on measurement of the complex transmission coefficient
of a plane-parallel sample with subsequent calculation of the spectra of its optical
parameters from those of the transmission coefficient amplitude Tr(ν) and the phase φ(ν). The corresponding expression can be written as
[22,23]

(1)

Here

(2)

are Fresnel coefficients for the interfaces ‘air–sample’, indices p, q=1, 2 correspond: ‘1’ to air (refractive index n1=1, extinction coefficient k1=0) and ‘2’ to the material of the sample (n2, k2),
d is the sample thickness, λ is the radiation wavelength. The sample parameters (for instance, n2 and k2 ) are found for each fixed frequency by solving two coupled equations for the two
unknowns, Tr(n2, k2, ν)=Trexp(ν) and φ(n2, k2, ν)=φexp(ν) [here Trexp(ν) and φexp(ν) are the measured quantities]. The so-found values of n2(ν) and k2(ν) can then be used to derive the spectra of the complex permittivity
, complex conductivity
, etc. (
is the high-frequency contribution to the permittivity).

If the sample is characterized by low enough absorption coefficient, Fabry–Perot-like
interference of the radiation within the plane-parallel layer leads to an interference
maxima and minima in the transmission coefficient spectra. In this case there is no
need to measure the phase shift spectra since the pairs of optical quantities of the
sample can be calculated from the transmission coefficient spectrum alone: the absorptive
part (like ε′ or σ1) is determined from the interferometric maxima amplitudes and the refractive part
(like ε′ or n) is calculated from their positions
[20,21].

When measuring the dielectric response of the films (like heterostructures in the
present case) on dielectric substrates, first the dielectric properties of the substrate
material are determined by standard techniques just described. Next, one measures
the spectra of the transmission coefficient and of the phase shift of the film-substrate
system, and it is these spectra that are used to derive the dielectric response of
the film by solving two coupled equations for two unknowns—“optical” parameters of
the film. The corresponding expression for the complex transmission coefficient of
a two-layer system can be written as
[22,23]:

(3)

where indices 1 and 4 refer to the media on the two sides of the sample, i.e., of
the film on substrate, δp=(np + ikp), with dp being the film and substrate thicknesses (p=2, 3). The other notations are the same as in Eq. (1). The measurements are performed
in a quasioptical configuration, no waveguides are used
[20,21] and this makes measurement schemes extremely flexible. All measurement and analysis
procedures are PC-controlled. Most important parameters of the BWO-spectrometer are
summarized in Table
1.

Results and discussion

Morphology and defects

STM and RHEED study of Ge/Si(001) QD arrays: morphology and formation

Previously, we have shown in a number of STM studies[9,11,12,24-26] that the process of the hut array nucleation and growth at low temperatures starts
from occurrence of two types of 16-dimer nuclei
[25] on wetting layer (WL) patches of 4-ML height
[26] giving rise to two known species of {105}-faceted clusters—pyramids and wedges
[9]—which then, growing in height (both types) and in length (wedges), gradually occupy
the whole wetting layer, coalless and start to form a nanocrystalline Ge film (Figure
2)
[11,12]. This is a life cycle of hut arrays at the temperatures < 600℃. We refer to cluster
growth at these temperatures as the low-temperature mode.

At high temperatures (> 600℃), only pyramids represent a family of huts: they were
found to nucleate on the WL patches in the same process of 16-dimer structure occurrence
as at low temperatures
[24]. We failed to find wedges or their nuclei if Ge was deposited at these temperatures
and this fact waits for a theoretical explanation.

In addition to pyramids, shapeless Ge heaps faceting during annealing have been observed
on WL in the vicinity of pits and interpreted as possible precursors of large faceted
clusters
[12,24]. Note that a mechanism of Ge hut formation via faceting of some shapeless structures
appearing near WL irregularities, which resembles the process described in the current
article, was previously considered as the only way of Ge cluster nucleation on Si(001)
[27,28]. Now we realize that huts nucleate in a different way
[25] and formation of the faceting heaps at high temperatures is a process competing with
appearance of real pyramidal huts which arise due to formation of the 16-dimer nuclei
on tops of WL patches
[11,25,26]. Yet, further evolution of the Ge heaps into finalized faceted clusters, such as
domes, in course of Ge deposition is not excluded
[24].

During further growth at high temperatures, pyramids reach large sizes becoming much
greater than their low-temperature counterparts and usually form incomplete facets
or split edges (Figure
3). An incomplete facet seen in Figure
3a and especially a “pelerine” of multiple incomplete facets seen in Figure
3b,c around the pyramid top indicate unambiguously that this kind of clusters grow
from tops to bottoms completing facets rather uniformly from apexes to bases, and
bottom corners of facets are filled the latest. Sometimes it results in edge splitting
near the pyramid base (Figure
3b,d).

Figure 3.STM empty-state images of high-temperature pyramids. Tgr=650℃; (a) 87×87 nm, steps of the incomplete upper left facet, running normal to the base side,
are seen near the left corner of the pyramid; (b) 87×87 nm, a cluster with edges split near the base and an apex formed by a set of
incomplete {105} facets; (c) 57×57 nm, a magnified image of a facet with several {105} incomplete facets near an
apex; (d) 22×22 nm, a split edge near a base.

RHEED has allowed as to carry our in-situ explorations of forming cluster arrays. We have compared RHEED patterns of Ge/Si(001)
surfaces during Ge deposition at different temperatures and a dynamics of diffraction
patterns during sample heating and cooling.

Diffraction patterns of reflected high-energy electrons for samples of thin (hGe= 4 Å) Ge/Si(001) films deposited at high (650 or 600℃) and low (360℃) temperatures
with equal effective thicknesses are presented in Figure
4a,b. The patterns are similar and represent a typical (2×1) structure of Ge WL; reflexes
associated with appearance of huts (the 3D-reflexes) are absent in both images, that
agrees with the data of the STM analysis. Diffraction patterns presented in Figure
4a,c,e are related to the samples with hGe increasing from 4 to 6 Å. The 3D-reflexes are observed only in the pattern of the
samples with hGe= 6 Å, that is also in good agreement with the STM data
[12,26].

Influence of the sample annealing at the deposition temperature is illustrated by
a complimentary pair of the RHEED patterns given in Figure
4c,d. Annealing of specimens at the temperature of growth (650℃) resulted in appearance
of the 3D-reflexes (Figure
4d) that also corresponds with the results of our STM studies
[12].

Difference in evolution of diffraction patterns during the deposition of Ge is a characteristic
feature of the high-temperature mode of growth in comparison with the low-temperature
one. The initial Si(001) surface before Ge deposition is (2×1) reconstructed. At high
temperatures, as hGe increases, diffraction patterns evolve as
(2×1) with very weak ½-reflexes. Brightness of the ½-reflexes gradually increases
(the (2×1) structure becomes pronounced) and the 3D-reflexes arise only during sample
cooling (Figure
5). At low temperatures, the RHEED patterns change as
(2×1) + 3D-reflexes. The resultant pattern does not change during sample cooling.

This observation reflects the process of Ge cluster “condensation” from the 2D gas
of mobile Ge adatoms. High Ge mobility and low cluster nucleation rate in comparison
with fluxes to competitive sinks of adatoms determines the observed difference in
the surface structure formation at high temperatures as compared with that at low
temperatures
[12,24] when the adatom flux to nucleating and growing clusters predominates and adatom (addimer)
mobility is relatively small.

STM and HRTEM study of Ge/Si heterostructures with QD array: morphology and defects

Structures overgrown with Si were examined by means of HRTEM for structural perfection
or possible defects, e.g., imperfections induced by array defects reported in Ref.
[29].

Data of HRTEM studies evidence that extended defects do not arise at low hGe on the buried Ge clusters and perfect epitaxial heterostructures with quantum dots
form under these conditions that enables the formation of defectless multilayer structures
suitable for device applications. Figure
6 relates to the five-layer Ge/Si structure with hGe = 6 Å. We succeeded to resolve separate Ge clusters whose height is, according to
our STM data
[9,12], ≲ 3 ML over WL patches (Figure
6a,b). A lattice structure next to the cluster apex is not disturbed (Figure
6c,d); its parameters estimated from the Fourier transform of an image taken from this
domain (Figure
6e,f), ∼5.4 Å along the [001] direction and ∼3.8 Å along [110], within the accuracy
of measurements coincide with the parameters of the undisturbed Si lattice.

Figure 6.HRTEM data for the five-layer Ge/Si heterostructure with buried Ge clusters. hGe = 6 Å (see Figure
2a); (a) a long shot, the mark is 100 nm; (b) Ge clusters resolved in a layer, figure ‘1’ indicates one of the clusters, ‘2’ shows
a WL segment; the mark is 50 nm; (c),(d) magnified images of a Ge cluster, the panel (d) corresponds to the light square in the panel (c); the marks are 10 and 5 nm, respectively; (e) a close-up image of a domain next to the top of the cluster imaged in (d); (f) the Fourier transform of the image (e), the measured periods are ∼5.4 Å along [001] and ∼3.8 Å along [110]; arrows in panels
(c) to (f) indicate the [001] direction.

Stacking faults (SF) have been found to arise above Ge clusters at hGe as large as 10 Å (Figure
7). SFs often damage Si structures with overgrown Ge layers at this values of hGe. A high perfection structure is observed around Ge clusters in Figure
7a although their height is up to 1.5 nm over WL (the typical height of huts is known
from both our STM and HRTEM data). Yet, a tensile strained domain containing such
extended defects as SFs and twin boundaries forms over a cluster shown in Figure
7b,c (twinning is clearly observable in Figure
7d). One can see, however, that this cluster is extraordinary high: its height over
WL exceeds 3.5 nm. Such huge clusters have been described by us previously as defects
of arrays
[29]; we predicted in that article such formations to be able to destroy Ge/Si structures
generating high stress fields in Si spacer layers and, as a consequence, introducing
extended defects in device structures. As seen in Figure
7b,c, the stress field spreads under the cluster in the Si buffer layer grown at much
higher temperature than the cap. Unfortunately, the huge Ge hut clusters (as we showed
in Ref.
[29], they are not domes) usually appear in the arrays and their number density was estimated
as ∼109 cm−3 from the STM data.

Strain domains are also seen next to Ge clusters in the five-layer structures depicted
in Figure
8 (hGe = 9 or 10 Å). We found that such domains are not inherent to all cluster vicinities
but only to some of them (Figure
8a,d). The disturbed strained domains give a contrast different from that of the undisturbed
Si lattice (Figure
8e). Zoom-in micrographs of the disturbed regions show perfect order of atoms in the
crystalline lattice (Figure
8b,c,e,f) everywhere except for the closest vicinities of the Si/Ge interface where
point defects and a visible lattice disordering immediately next to the cluster are
registered (Figure
8b,c,e,f). However, some farther from the interfaces but still near cluster apexes
the crystalline order restores (Figure
8h). We have estimated the lattice parameter in the disturbed regions from the Fourier
transforms of the HRTEM micrographs taken in these domains (Figure
8i). The values we obtained appeared to vary for different regions. Yet, they usually
appreciably exceeded the Si lattice parameter. Moreover, they often reached the Ge
parameter of ∼ 5.6–5.7 Å (along [001] and ∼ 4 Å along [110]). This might be explained
either by appreciable diffusion of Ge from clusters (previously, we have already reported
an appreciable diffusion of Si in Ge clusters in analogous structures from covering
Si layers grown at 530℃
[30,31]) or by Si lattice stretching under the stress. Likely both factors act.

Figure 8.TEM data for the five-layer Ge/Si heterostructures, Tgr = 360℃. (a) to (c) hGe = 9 Å; (d) to (i) hGe = 10 Å; (a) domains of tensile strain in Si over Ge clusters are observed more or less distinctly
near most clusters, but not around all; the surface is down; the mark equals 20 nm;
(b), (c) zoom in two strained domains, no extended defects are observed; (d) strained domains are more pronounced, the strain is well recognized even under some
clusters; (e) a magnified image of a strained domain; a strained lattice is well contrasted with
the normal one; (f) zoom in the dilated lattice, a perfectly ordered lattice is observed; (g) a Si domain next to the Ge/Si interface near the cluster apex, a vacancy (‘V’) and
disordered lattice (upper right corner) are revealed; letter ‘I’ indicates the direction
to the interface along <11
>; (h) the same as in (g) but some farther from the interface, the lattice is perfect; (i) the Fourier transform of an image obtained from a strained domain demonstrates an
enhanced lattice parameter (the strain varies from domain to domain, the estimated
lattice period in the [001] direction sometimes reaches ∼ 5.6 Å).

It is worth while emphasising that the stretched domains usually do not contain extended
defects, as it is seen from the HRTEM micrographs, except for the cases of array defects
(huge clusters) like that demonstrated in Figure
7. We suppose that the extended defects in these regions arise because the strain exceeds
an elastic limit near huge clusters.

Finally, we have tried to find out if huge clusters exist in arrays of hGe=9 Å (Figure
9). We have been convinced that even in rather uniform arrays large clusters (Figure
9e), which might generate considerable stress, are abundant and even huge ones (Figure
9d), which should produce lattice disordering (extended defects), are available. Effect
of such defects as huge clusters on device performance and a cause of their appearance
in hut arrays await further detailed studies.

Photo-emf of Ge/Si p–i–n-structures

Photo-emf spectra

We have investigated heteroepitaxial Si p–i–n-diodes with multilayer stacks of Ge/Si(001) QD dense arrays built in intrinsic domains
and found them to exhibit the photo-emf in a wide spectral range from 0.8 to 5 μm
[32,33]. An effect of wide-band irradiation by infrared light on the photo-emf spectra has
been observed. Here we describe the most representative data obtained for two radically
different structures denoted as R 163 and R 166 (Figure
1).

Typical photo-emf spectra obtained for R 163 and R 166 structures are presented in
Figure
10. In the spectra, we mark out three characteristic ranges which differently respond
to bias lighting and differently depend on its power.

(i) Wavelength range from 0.8 to 1.0 μm. The photo-emf response increases with the increase in the bias lighting power, reaches
maximum at P≈0.63 mW/cm2 with a Si filter and at P≈2.6 mW/cm2 with a Ge filter and decreases with further increase in the power.

(ii) Wavelength range from 1.1 to 2.6 μm. The photo-emf response decreases monotonously in this range with the increase in
the power of the bias lighting with any, Si or Ge, filter.

(iii) Wavelength range > 2.6 μm. The photo-emf response increases with the increase in the bias lighting power and
comes through its maximum at P≈0.63 mW/cm2 if a Si filter is used and at P≈0.25 mW/cm2 for a Ge filter. The response decreases with further growth of the bias lighting
power for a Si filter and remains unchanged when Ge filter is utilized.

We propose the following model for explanation of these observations: In the studied
structures, all QD layers are located in the i-domain (Figure
11). One can see from these sketches that some QD layers are positively charged (the
ground states of QDs is above the Fermi level and hence they are filled by holes)
while others are neutral (the QDs’ ground states are below Fermi level and hence empty).
Then, one may consider a QD layer as a single ensemble of interacting centers because
the average distance between QDs’ apexes is about 13 nm whereas QDs’ bases adjoin.
Consequently, one can imagine an allowed energy band with some bandwidth, determined
by QDs’ sizes and composition dispersion, and a certain density of states in this
band. Let us explore in detail every range of the photo-emf spectra taking into account
the proposed model.

Figure 11.Schematics of band structures of the Sip–i–n-diodes with Ge QD arrays represented in Figure 1. (a) R 163, (b) R 166; figures ‘1’, arrows and wavy lines indicate potential barriers for holes in
the valence band (Ev) which are associated with the Ge QD arrays; black and shaded parts of potential
wells show bands of filled (above the Fermi level F) and empty (below F) energy levels in the QD ensemble; two vertical wavy lines in panel (b) indicate
a gap in the drawing of a very thick buffer layer of Si (1690 nm) deposited on the
n-Si substrate.

Wavelength range from 0.8 to 1.0 μm

Without bias lighting, all radiation in the Si fundamental absorption range can be
believed to be absorbed in Si (cap-layer, spacers, buffer layer and substrate) and
QDs are not involved in the absorption, so the total charge of QD layers remains unaltered.
Electron-hole pairs are generated in the intrinsic region of the p–i–n-diode as a result of the absorption and separated by the junction field which converts
the radiation to emf. However, carrier separation is hindered because of presence
of the potential barriers for holes in the valence band which are produced by the
charged QD layers situated in intrinsic domain. Calculated height of these barriers
equals 0.1 to 0.2 eV depending on the layer position in the structure.

Transitions from QD ensemble states to the valence and conduction bands of Si start
under bias lighting. Carriers excited by bias lighting do not contribute to the photo-emf
signal measured at the modulation frequency of the narrow-band radiation. QDs captured
a photon change their charge state. An effective layer charge decreases as a result
of the absorption of the bias lighting radiation that results in reduction of potential
barrier height and more efficient carrier separation in the junction field. Increase
in the photo-emf response in the fundamental absorption range under bias lighting
is explained by this process.

Wavelength range from 1.1 to 2.6 μm

This band is entirely below the Si fundamental absorption range. Therefore the response
in this region cannot be explained in terms of absorption in bulk Si. One can explain
the presence of the photo-emf signal in this region considering the following model:
Both hole transitions from the QD ensemble states to the valence band and electron
transitions from the QD ensemble states to the conduction band due to absorption of
photons with the energy between ∼1.12 and ∼0.4 eV are possible. The probability of
every kind of the transitions is determined by the photon energy, the density of states
in the QD ensemble and by effective charge of the QD layer.

It follows from theoretical studies
[34,35] and experiments on photoluminescence
[36,37] that photons with energies ranged from 0.7 to 0.9 eV are required for electron transitions
from the QD states to the conduction band. However, it is necessary to mention the
research of photoconductivity
[38], in which electron transitions for low photon energy (∼0.4 eV) have been shown to
be likely. The availability of these transitions is explained by dispersion of sizes
and composition of QDs, effect of diffusion on the hetero-interface and deformation
effects.

The likelihood of electron transitions drops rapidly with photon energy decrease because
of reduction of the density of states in the QDs ensemble when approaching to the
conduction band edge. This is the reason of the observed monotonous decrease in the
photo-emf signal with the increase in the radiation wavelength in this range.

At the same time, bias lighting switching on leads to growth of concentration of the
unmodulated (“dark”) carrier, depletion of QDs and as a consequence to the observed
reduction of the photo-emf response at the chopping frequency.

Wavelength range > 2.6 μm

As mentioned above, electron transitions can happen at low energy of the exciting
radiation (∼ 0.4 eV) which correspond to wavelength of ∼ 3.1 μm. Yet, the photo-emf signal is observed at the radiation wavelengths up to 5 μm in our measurements. The presence of the photo-emf response in this range can only
be explained if the QD layer is considered as a single ensemble of mutually interacting
centers. An effective positive charge in the QD layer forms a potential well for electrons
in the conduction band. This leads to reduction of energy needed for electron transitions
from the QD ensemble states to the conduction band. Partial emptying of the states
makes electron transitions possible and, at the same time, does not lead to significant
change in the potential wells depth. As a result, electron transitions can happen
at the exciting radiation energies as low as 0.25 eV. Hole transitions also can happen
at these energies via a large number of excited states in the QD ensemble.

It may be concluded that the likelihood of the electron transitions decreases faster
than that of the hole transitions as the exciting radiation energy decreases in the
considered wavelength range. However, first it is necessary to empty the levels by
the electron transitions to make possible hole transitions. This could be achieved
by using an additional radiation of the spectral domain where the probability of the
electron transitions is high. So, bias lighting stimulates the hole transitions by
exciting electrons that leads to emptying the levels. In this case the electron concentration
is not modulated as distinct from the hole concentration which is modulated at the
chopper frequency. This explains the observed low magnitude of the photo-emf in the
wavelength range > 2.6 μm and its increase under bias lighting.

Influence of buffer layer thickness on photo-emf spectra

As seen from Figure
11, the buffer layer thickness determines the QD layers position the in intrinsic domain
and thus controls the relative position of the Fermi level and the mini-band of the
QD array in the region where the QD layers are situated. The charge of the QD layer
is determined by the band occupation of the QD ensemble which, in turn, is controlled
by the Fermi level location. For this reason the effect of bias lighting on photo-emf
generated by the narrow-band radiation in the fundamental absorption range is much
stronger for the R 166 structure, which have a thick buffer layer, than for the R
163 one. This is clearly seen in Figure
12. The absolute value of photo-emf in the R 166 structure is lower than that in the
R 163 sample due to higher potential barriers for holes in the valence band. Yet,
the photo-emf response increases with the growth of the bias lighting power much stronger
in the R 166 p–i–n-diode than in the R 163 one.

Figure 12.Dependence of photo-emf response of the R 163 and R 166 p–i–n-structures on bias lighting power density. The experimental conditions are the same as in Figure
10.

Prospective photovoltaic IR detectors

On the basis of our results on the photo-emf in the Si p–i–n-structures with Ge quantum dots, we have recently proposed
[39] a new design of photovoltaic quantum dot infrared photodetectors which enables detection
of variations of photo-emf produced by the narrow-band radiation in the Si fundamental
absorption range (a reference beam) under the effect of the wide-band IR radiation
inducing changes in the Coulomb potential of the quantum dot ensemble which, in turn,
affects the efficiency of the photovoltaic conversion of the reference beam. The quantum
dot array resembles a grid of a triode in these detectors which is controlled by the
detected IR light. The reference narrow-band radiation generates a potential between
anode and cathode of this optically driven quantum dot triode; a magnitude of this
voltage depends on the charge of the QD grid (Figure
11). Such detectors can be fabricated on the basis of any appropriate semiconductor
structures with potential barriers, e.g., p–i–n-structures, pn-junctions or Schottky barriers, and built-in arrays of nanostructures.

There are many ways to deliver the reference beam to the detector, e.g., by irradiating
the sensor by laser or LED. We propose, however, surface plasmon polaritons delivered
to the detector structures by the plasmonic waveguides
[40,41] to be applied as the reference beams in the detector circuits. This approach makes
such detectors, if based on Si, fully compatible with existing CMOS fabrication processes
[42] that, in turn, opens a way to development of plasmonic IR detector arrays on the
basis of the monolithic silicon technology.

THz conductivity of multilayer Ge/Si QD arrays

The effective dynamic conductivity of Ge quantum dot layer was determined by measuring
the transmission coefficient spectra of heterostructures grown on Si(001) substrates.
Characteristics of the substrates were determined beforehand as demonstrated by Figure
13 and Figure
14. In Figure
13, the interferometric pattern in the transmission coefficient spectrum Tr(ν) of a plane-parallel Si substrate is clearly seen. Pronounced dispersion of Tr(ν) peaks and their temperature dependence allow to extract the parameters of the charge
carriers (holes) by fitting the spectra with Eq. (2) and by modelling the sample properties
with the Drude conductivity model where the complex AC conductivity is given by an
expression
[23,43]

(4)

Figure 13.Spectra of transmission coefficient of a silicon substrate (a commercial wafer, ρ=12 Ω cm), measured at two temperatures using two different BWO working in spectral
ranges from 11 cm−1 to 24 cm−1 and from 29 cm−1 to 39 cm−1. Dots show the measurement results, lines are least-square fits based on the Drude
conductivity model, as described in the text.

Figure 14.Temperature dependences of the silicon substrate parameters obtained by fitting the
transmission coefficient spectra as shown in Figure 13 and described in the text. (a) plasma frequency of charge carriers and (b) scattering rate. Solid line in (b) shows the T−3/2 behavior.

Here σ1 is the real part and
is the imaginary part of the conductivity,
is the high-frequency dielectric constant,
is the DC conductivity,
is the plasma frequency of the carriers condensate, n, e and m∗ are, respectively, their concentration, charge and effective mass and γ is their scattering rate. Figure
14 shows the temperature variation of the plasma frequency and the scattering rate of
charge carriers. Lowering of the plasma frequency is mainly connected with the carriers’
freezing out and the γ(T) behaviour is well described by a
dependence, as expected.

The values of effective dynamical conductivity and absorption coefficient α=4πk/λ of the heterostructures with Ge quantum dots were determined basing on the measurements
of terahertz transmission coefficient spectra of the Si substrate with the heterostructure
on it as compared to the spectra of the same substrate with the heterostructure etched
away; this allowed us to avoid influence of (even slight) differences in dielectric
properties of substrates cut of a standard commercial silicon wafer. By comparing
the so-measured transmissivity spectra we reliably detect, although small, changes
in the amplitudes of interference maxima of a bare substrate caused by heterostructures.
This is demonstrated by Figure
15: at T=300 K we clearly and firmly register a 2% lowering of the peak transmissivity introduced
by the heterostructure. When cooling down, the difference decreases and we were not
able to detect it below about 170 K, see Figure
16. Correspondingly, as is seen in Figure
16, the AC conductivity of the heterostructure decreases while cooling, along with the
conductivity of the Si substrate. The latter observation might be an indication of
the fact that the charges are delivered into the quantum dot array from the substrate;
the statement, however, needs further exploration.

Figure 15.Spectra of transmission coefficient of Ge/Si heterostructure on Si substrate (solid
symbols) and of bare substrate (open symbols) measured at two different temperatures. Horizontal lines show the difference in peak transmissivity that is observed at 300
K and disappears at ∼ 170 K. The peaks positions are shifted due to slight difference
in the Si substrate thickness.

Figure 16.Temperature dependences of dynamical conductivity of Ge/Si heterostructure and of
Si substrate. Frequency is around 1 THz.

Measuring the room temperature spectra, we have found that the AC conductivity and
the absorption coefficient of the heterostructure do not depend on the effective thickness
(measured by the quartz sensors during MBE) of the germanium layer (hGe) for hGe ranging from 8 to 14 Å, see Figure
17. For larger coverage, hGe>14 Å, both quantities start to decrease.

One of the main findings of this work is that the AC conductivity and absorption coefficient
of Ge/Si heterostructures have been discovered to be significantly higher than those
of the structure with the same amount of germanium not organized in an array of quantum
dots. Crucial role played by quantum dots is supported by a decrease of σAC and α observed for large germanium coverage (hGe > 14 Å), when structurization into quantum dots gets less pronounced and the thickness
of Ge layer becomes more uniform. On the other hand, it is worth noting that no extra
absorption of terahertz radiation was detected in the samples with low coverage, hGe=4.4 and 6 Å. This can be explained either by the absence of quantum dots in that
thin Ge layer or by their small sizes, by a large fraction of the free wetting layer
or by relatively large distances between the clusters as compared to their sizes,
i.e., by the absence or smallness of the effect of quantum dots on the dielectric
properties of the heterostructure.

As seen from Figure
17, the values
and α≈4000 cm−1 are considerably higher than the values measured for bulk germanium, σAC(Ge)≈10−2 Ω−1cm−1, by about four orders of magnitude, and α(Ge)≈40 cm−1, by about two orders of magnitude. Assuming that the AC conductivity of heterostructure
is connected with the response of (quasi) free carriers, one can express it with a
standard formula σ=eμn=ne2(2πγm∗)−1(μ is the mobility of charge carriers). Then, the observed increase has to be associated
with considerable enhancement either of the mobility (suppression of scattering rate)
of charge carriers within a quantum dot array or of their concentration. The second
possibility has to be disregarded since the total concentration of charges in the
sample (substrate plus heterostructure) remains unchanged. As far as the mobility
increase is concerned, we are not aware of a mechanism that could lead to its orders
of magnitude growth when charges get localized within the quantum dot array.

Another interpretation of the observed excess AC conductivity could be based on some
kind of resonance absorption of terahertz radiation. Known infrared experiments exhibit resonances
in quantum dot arrays that are caused by the transitions between quantized energy
levels, as well as between the split levels and the continuum of the valence or conduction
band
[4,44-47]. Carriers localized within quantum dots can form bound states with the carriers in
the surrounding continuum (excitons) or with optical phonons (polarons), which can
in turn interact with each other and form collective complexes
[3,4,45-48]. Plasma excitations generated by electromagnetic radiation in the assembly of conducting
clusters or quantum dots also have energies of about 10 meV
[49-51], i.e., fall into the THz band. It is important that these effects can be observed
not only at low, but at elevated temperatures as well, up to the room temperature.
At this stage, we are not able to unambiguously identify the origin of the THz absorption
seen at T=170 to 300 K in Ge/Si heterostructure with Ge quantum dots. Among the aforementioned,
the mechanisms involving polaritons or plasma excitations seem to be least affected
by thermal fluctuations and could be considered as possible candidates. To get detailed
insight into microscopic nature of the observed effect, further investigations of
heterostructures with various geometric and physical parameters, as well as in a wider
frequency and temperature intervals are in progress.

Conclusions

In conclusion of the article, we highlight its main provisions.

Using high resolution STM and in-situ RHEED we have explored the processes of Ge hut cluster array formation and growth
at low temperatures on the Ge/Si(001) wetting layer. Different dynamics of the RHEED
patterns in the process of Ge hut array formation at low and high temperatures of
Ge deposition reflects the difference in adatom mobility and their fluxes from 2D
gas of mobile particles (atoms, dimers and dimer groups) on the surface which govern
the nucleation rates and densities of arising Ge clusters.

HRTEM studies of multilayer Ge/Si heterostructures with buried arrays of Ge huts have
shown that the domains of stretched lattice occurring over Ge clusters in Si layers
at high Ge coverages usually do not contain extended defects. We suppose that the
extended defects in these regions arise because the strain exceeds an elastic limit
near huge clusters.

Silicon p–i–n-diodes with multilayer stacks of Ge cluster arrays built in i-domains have been found to exhibit the photo-emf in a wide spectral range from 0.8
to 5 μm. A significant increase in photo-emf response in the fundamental absorption range
under the wide-band IR radiation has been reported and explained in terms of positive
and neutral charge states of the quantum dot layers and the Coulomb potential of the
quantum dot ensemble. A new type of photovoltaic QDIPs is proposed in which photovoltage
generated by a reference beam in the fundamental absorption band is controlled by
the QD grid charge induced by the detected IR radiation
[39].

Using a BWO-spectrometer, first measurements of terahertz dynamical conductivity spectra
of Ge/Si heterostructures were carried out at frequencies ranged from 0.3 to 1.2 THz
in the temperature interval from 5 to 300 K. The effective dynamical conductivity
of the heterostructures with Ge quantum dots has been found to be significantly higher
than that of the structure with the same amount of Ge not organized in quantum dots.
The excess conductivity is not observed in the structures with the Ge coverage less
than 8 Å. When a Ge/Si sample is cooled down the conductivity of the heterostructure
decreases.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

VAY conceived of the study and designed it, performed data analysis, and took part
in discussions and interpretation of the results; he also supervised and coordinated
the research projects. LVA participated in the design of the study, carried out the
experiments, performed data analysis, and took part in discussions and interpretation
of the results. MSS investigated the photo-emf spectra; he carried out the experiments,
performed data analysis, and took part in discussions and interpretation of the results.
VAC participated in the design of the study, took part in discussions and interpretation
of the results; he also supervised the researches performed by young scientists and
students. KVC took pat in the experiments on investigation of the photo-emf spectra
and the terahertz conductivity; he prepared experimental samples and took part in
discussions and interpretation of the results. OVU performed the HRTEM studies and
took part in discussions and interpretation of the results. VPK participated in the
design of the study, took part in discussions and interpretation of the results; he
also supervised the research project. ESZ carried out the experiments on the terahertz
spectroscopy; she performed measurements and data analysis, and took part in discussions
and interpretation of the results. ASP participated in the studies by the terahertz
spectroscopy; he took part in discussions and interpretation of the results. IES participated
in the studies by the terahertz spectroscopy; he took part in discussions and interpretation
of the results. BPG performed the explorations by the terahertz spectroscopy; he participated
in the design of the study, performed measurements and data analysis, and took part
in discussions and interpretation of the results; he also supervised the research
project. All authors read and approved the final manuscript.

Acknowledgements

This research has been supported by the Ministry of Education and Science of RF through
the contracts No. 14.740.11.0069 and 16.513.11.3046 and by RFBR through the grant
No. 11-02-12023-ofi-m. Equipment of the Center of Collective Use of Scientific Equipment
of GPI RAS was utilized for this study. We acknowledge the financial and technological
support of this work.

We express our appreciation to Ms. Natalya Kiryanova for her valuable contribution
to organization and management of this research.